Glyphs for General Second-Order 2D and 3D Tensors

Four-Dimensional Visualization of Topological Fixed Points in Pulsatile Cardiovascular Flows

Topological features of time-dependent, three-dimensional (3D) vector flow fields, such as wall shear stress (WSS) fixed points, are considered surrogates of pathological blood flow dynamics in cardiovascular diseases. Fixed-point visualizations are typically constrained to two-dimensional (2D) spaces, yet they aim to display complex spatiotemporal (four-dimensional (4D)) dynamics. There is a need for visualization strategies to reduce occlusion and reliance on animations to allow the detection of holistic flow patterns. Using intracranial aneurysms as a use case, we present the fixed-point carousel, a novel approach to visually depicting the "4D" nature of WSS fixed points via (1) topographic mapping of the 3D aneurysm sac to overcome occlusion while preserving fixed-point distances and sac morphological features; and (2) arranging these into a carousel model to present with temporal dimension holistically. Examples are presented for image-based computational fluid dynamic (CFD) models of intracranial aneurysms, illuminating the intricate and distinct fixed-point trajectories and interactions, a necessary step toward understanding the volumetric flow manifolds that drive them for this and other cardiovascular-and potentially nonbiomedical-fluid dynamics applications.

Evaluating Glyph Design for Showing Large-Magnitude-Range Quantum Spins

We present experimental results to explore a form of bivariate glyphs for representing large-magnitude-range vectors. The glyphs meet two conditions: (1) two visual dimensions are separable; and (2) one of the two visual dimensions uses a categorical representation (e.g., a categorical colormap). We evaluate how much these two conditions determine the bivariate glyphs' effectiveness. The first experiment asks participants to perform three local tasks requiring reading no more than two glyphs. The second experiment scales up the search space in global tasks when participants must look at the entire scene of hundreds of vector glyphs to get an answer. Our results support that the first condition is necessary for local tasks when a few items are compared. But it is not enough for understanding a large amount of data. The second condition is necessary for perceiving global structures of examining very complex datasets. Participants' comments reveal that the categorical features in the bivariate glyphs trigger emergent optimal viewers' behaviors. This work contributes to perceptually accurate glyph representations for revealing patterns from large scientific results. We release source code, quantum physics data, training documents, participants' answers, and statistical analyses for reproducible science at https://osf.io/4xcf5/?view_only=94123139df9c4ac984a1e0df811cd580.

Electromechanical Coupling in Electroactive Polymers - a Visual Analysis of a Third-Order Tensor Field

Electroactive polymers are frequently used in engineering applications due to their ability to change their shape and properties under the influence of an electric field. This process also works vice versa, such that mechanical deformation of the material induces an electric field in the EAP device. This specific behavior makes such materials highly attractive for the construction of actuators and sensors in various application areas. The electromechanical behaviour of electroactive polymers can be described by a third-order coupling tensor, which represents the sensitivity of mechanical stresses concerning the electric field, i.e., it establishes a relation between a second-order and a first-order tensor field. Due to this coupling tensor's complexity and the lack of meaningful visualization methods for third-order tensors in general, an interpretation of the tensor is rather difficult. Thus, the central engineering research question that this contribution deals with is a deeper understanding of electromechanical coupling by analyzing the third-order coupling tensor with the help of specific visualization methods. Starting with a deviatoric decomposition of the tensor, the multipoles of each deviator are visualized, which allows a first insight into this highly complex third-order tensor. In the present contribution, four examples, including electromechanical coupling, are simulated within a finite element framework and subsequently analyzed using the tensor visualization method.

An Analytical Method for Tensor Visualization in a Plane

The rendering of tensor glyphs is a progressive process of visualizing the vector space both in fluid dynamics and the latest medical scanning. Nowadays, the rendering accuracy is ensured by numerical methods based on interpolation of tensor functions. The tensor glyph functions to visualize significant properties of the vector space. Not all these properties are visualized at all times. The number of properties and their unambiguity depend on the method chosen. This work presents a direct analytical expression covering rank two tensors in a plane. Unlike the methods used so far, this method is accurate and unambiguous one for tensor visualization. The method was applied to the simplest tensor type, which presented an advantage for the method’s analytical approach. The analytical approach to the planar case is significant also because it provides instruction on how to expand analytical calculations to cover higher spatial dimensions. In this way, numerical methods for tensor rendering can be replaced with an accurate analytical method.

Feature Curves and Surfaces of 3D Asymmetric Tensor Fields

3D asymmetric tensor fields have found many applications in science and engineering domains, such as fluid dynamics and solid mechanics. 3D asymmetric tensors can have complex eigenvalues, which makes their analysis and visualization more challenging than 3D symmetric tensors. Existing research in tensor field visualization focuses on 2D asymmetric tensor fields and 3D symmetric tensor fields. In this paper, we address the analysis and visualization of 3D asymmetric tensor fields. We introduce six topological surfaces and one topological curve, which lead to an eigenvalue space based on the tensor mode that we define. In addition, we identify several non-topological feature surfaces that are nonetheless physically important. Included in our analysis are the realizations that triple degenerate tensors are structurally stable and form curves, unlike the case for 3D symmetric tensors fields. Furthermore, there are two different ways of measuring the relative strengths of rotation and angular deformation in the tensor fields, unlike the case for 2D asymmetric tensor fields. We extract these feature surfaces using the A-patches algorithm. However, since three of our feature surfaces are quadratic, we develop a method to extract quadratic surfaces at any given accuracy. To facilitate the analysis of eigenvector fields, we visualize a hyperstreamline as a tree stem with the other two eigenvectors represented as thorns in the real domain or the dual-eigenvectors as leaves in the complex domain. To demonstrate the effectiveness of our analysis and visualization, we apply our approach to datasets from solid mechanics and fluid dynamics.

Visualization of 3D Stress Tensor Fields Using Superquadric Glyphs on Displacement Streamlines

Stress tensor fields play a central role in solid mechanics studies, but their visualization in 3D space remains challenging as the information-dense multi-variate tensor needs to be sampled in 3D space while avoiding clutter. Taking cues from current tensor visualizations, we adapted glyph-based visualization for stress tensors in 3D space. We also developed a testing framework and performed user studies to evaluate the various glyph-based tensor visualizations for objective accuracy measures, and subjective user feedback for each visualization method. To represent the stress tensor, we color encoded the original superquadric glyph, and in the user study, we compared it to superquadric glyphs developed for second-order symmetric tensors. We found that color encoding improved the user accuracy measures, while the users also rated our method the highest. We compared our method of placing stress tensor glyphs on displacement streamlines to the glyph placement on a 3D grid. In the visualization, we modified the glyph to show both the stress tensor and the displacement vector at each sample point. The participants preferred our method of glyph placement on displacement streamlines as it highlighted the underlying continuous structure in the tensor field.

Artificial intelligence in critical care: Its about time!

Currently, most critical care information is not expressed automatically at a granular level, rather is continually assessed by overindulged Intensive Care Unit (ICU) staff. Furthermore, due to different confounding morbidities and the uniqueness of the ICU setting, it is difficult to protocolize treatment regimens in the ICU. In highly complex ICU setting where man and resource management becomes extremely challenging, definite advancements are required to implement Artificial Intelligence (AI) for prognosticating the course of the disease to aid in informed decision-making. AI is the intelligence of a computer or computer-supervised robot to execute a piece of work commonly associated with intelligent beings, wherein the machines go beyond the realms of normal information processing by adding the characteristics of learning, sound reasoning, and weighting of the inputs. AI recognizes circuitous, relational time-series blueprint within datasets and this reasoning of analysis transcends conventional threshold-based analysis adapted in ICU protocols. AI works on the principle of a more complex form of Machine Learning by Artificial Neural Networks (ANN). These information-processing paradigms use multidimensional arrays called tensors which aid in 'learning' and 'weighting' all the information made available to it, thereby converting normal machine learning into Deep Learning. Here, the use of AI for data mining in complex ICU settings for protocol formulation and temporal representation and reasoning is discussed.

Multi-Scale Topological Analysis of Asymmetric Tensor Fields on Surfaces

Asymmetric tensor fields have found applications in many science and engineering domains, such as fluid dynamics. Recent advances in the visualization and analysis of 2D asymmetric tensor fields focus on pointwise analysis of the tensor field and effective visualization metaphors such as colors, glyphs, and hyperstreamlines. In this paper, we provide a novel multi-scale topological analysis framework for asymmetric tensor fields on surfaces. Our multi-scale framework is based on the notions of eigenvalue and eigenvector graphs. At the core of our framework are the identification of atomic operations that modify the graphs and the scale definition that guides the order in which the graphs are simplified to enable clarity and focus for the visualization of topological analysis on data of different sizes. We also provide efficient algorithms to realize these operations. Furthermore, we provide physical interpretation of these graphs. To demonstrate the utility of our system, we apply our multi-scale analysis to data in computational fluid dynamics.